The hung parliament British voters chose on Thursday should not be treated as a threat or a sign of national weakness. It is an opportunity. The 2010 result contained rewards and problems for each party. But it is a much better reflection than other recent elections, though still a distorted one, of the pluralist, multiparty society Britain has increasingly become. It is no longer a country in which every citizen is simply either a Labour or Conservative supporter. On Thursday, for the first time in generations, the two large parties took less than two-thirds of the votes. This week's result, therefore, offers a rare chance to mend the distortions altogether and create an electoral system which properly and enduringly reflects the country we actually are. Such moments do not often come around. It is a moment that must be seized.

Yesterday, both David Cameron and Gordon Brown emerged to make post-election statements which belatedly recognised the need to make political alliances to ensure stable government. There were impressive aspects to both. Mr Cameron was direct and detailed, setting out a menu of possibilities to the Liberal Democrats in the search for a stable majority. Mr Brown was more focused and statesmanlike as he sought to create space for Labour, though voted out of power, to offer a deal of its own. The statements unmistakably marked the crossing of a Rubicon between an old system in which the two main parties pretended that they alone represent the politics of the country and a new system, in which all the parties are compelled by plural realities to treat one another with respect and seek grownup agreements and compromises. Amid Thursday night's many disappointments, this is something to cheer.

The Conservatives' strong showing entitled them to make the first moves in deal-making. Mr Cameron called his offer big, open and comprehensive. In fact it was modest, conditional and limited. It was also extremely unspecific about the nature of the agreement that the Conservatives, with their large increase in votes and seats, are willing to offer the Liberal Democrats, with their modest increase in votes and slight drop in seats. Seats in the cabinet? Mr Cameron did not say. The issue is presumably on the table this weekend. What Mr Cameron did say, however, was that he would make no compromise with Nick Clegg on Europe, immigration or defence policy, was prepared to deal on education, a low carbon economy (as though any party favours a high-carbon one) and tax cuts, and would concede an all-party committee on electoral and political reform, while remaining committed to first past the post. Tory and Liberal Democrat teams were due to talk last night. But it would be extraordinary if Mr Clegg were to parlay the hopes of a quarter of the electorate for such a thin offer.

There are problems of a different nature for Mr Clegg with the options sketched out by Mr Brown. Labour, after all, was a big loser on Thursday. Having governed for 13 years, the party lost a net 91 seats and finished on 29% of the vote, its second worst share in the universal suffrage era. The invitation to Mr Clegg is therefore an invitation to the Liberal Democrats to prop up a government and prime minister who have just been defeated. Yet the invitation is legitimate in other ways, not least and crucially because the two parties between them have a majority of all votes cast and also more seats than the Conservatives. Mr Brown personally now has a mandate to share power, though not to govern alone, which he lacked before 6 May. Any such power-sharing deal – and power-sharing is a useful and positive way of thinking about such an alliance – would involve making many more concessions to the Liberal Democrats on items of policy than Mr Brown has yet set out, and might need to be extended to some of the minor parties, too. Nevertheless, Labour's offer is substantial and radical in ways that the Conservative offer is not. Above all, it sets electoral and political reform openly as one of the centrepieces of a potential programme of reform. Much more is needed, including a formal national unity coalition offer which treats all the parties that sign up to it more nearly as equals, as well as further concessions on such subjects as ID cards. The terms of the electoral reform package must be broadened, too. The long-term position of Mr Brown, whose public standing might weaken the chances of a yes vote in any reform referendum, must also be addressed with realism.

The difficulties of such a deal cannot be dismissed. There should be no denial about the sacrifices to be made on both sides, nor about the onslaught that would be made against it by reactionaries. Yet in multiparty politics, pacts between parties that speak for a majority of voters are always legitimate. And this opportunity is too important to be squandered. This weekend, Labour and the Liberal Democrats should strike a fixed-term deal to secure the economic recovery, assure the markets about key spending plans and hold an early referendum on electoral reform, with a general election on the new system to follow. The 2010 general election was a vote against the old politics. The Liberal Democrats and Labour must now seize the hour and finish the job.

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